### Abstract

We study the lattice effects on the simple holographic toy model; massive U(1) gauge theory for the bulk action. The mass term is for the U(1) gauge symmetry breaking in the bulk. Without the lattice, the AC conductivity of this model shows similar results to the holographic superconductor with the energy gap. On this model, we introduce the lattice effects, which induce the periodic potential and break the translational invariance of the boundary field theory. Without the lattice, due to the translational invariance and the mass term, there is a delta function peak at zero frequency on the AC conductivity. We study how this delta function peak is inuenced by the lattice effects, which we introduce perturbatively. In the probe limit, we evaluate the perturbative corrections to the conductivities at very small frequency limit. We find that the delta function peak remains, even after the lattice effects are introduced, although its weight reduces perturbatively. We also study the lattice wavenumber dependence of this weight. Our result suggests that in the U(1) symmetry breaking phase, the delta function peak is stable against the lattice effects at least perturbatively.

Original language | English |
---|---|

Article number | 117 |

Journal | Journal of High Energy Physics |

Volume | 2012 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2012 |

### Fingerprint

### Keywords

- AdS-CFT Correspondence
- Gauge-gravity correspondence
- Holography and condensed matter physics (AdS/CMT)

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2012*(11), [117]. https://doi.org/10.1007/JHEP11(2012)117

**Towards the lattice effects on the holographic superconductor.** / Iizuka, Norihiro; Maeda, Kengo.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2012, no. 11, 117. https://doi.org/10.1007/JHEP11(2012)117

}

TY - JOUR

T1 - Towards the lattice effects on the holographic superconductor

AU - Iizuka, Norihiro

AU - Maeda, Kengo

PY - 2012

Y1 - 2012

N2 - We study the lattice effects on the simple holographic toy model; massive U(1) gauge theory for the bulk action. The mass term is for the U(1) gauge symmetry breaking in the bulk. Without the lattice, the AC conductivity of this model shows similar results to the holographic superconductor with the energy gap. On this model, we introduce the lattice effects, which induce the periodic potential and break the translational invariance of the boundary field theory. Without the lattice, due to the translational invariance and the mass term, there is a delta function peak at zero frequency on the AC conductivity. We study how this delta function peak is inuenced by the lattice effects, which we introduce perturbatively. In the probe limit, we evaluate the perturbative corrections to the conductivities at very small frequency limit. We find that the delta function peak remains, even after the lattice effects are introduced, although its weight reduces perturbatively. We also study the lattice wavenumber dependence of this weight. Our result suggests that in the U(1) symmetry breaking phase, the delta function peak is stable against the lattice effects at least perturbatively.

AB - We study the lattice effects on the simple holographic toy model; massive U(1) gauge theory for the bulk action. The mass term is for the U(1) gauge symmetry breaking in the bulk. Without the lattice, the AC conductivity of this model shows similar results to the holographic superconductor with the energy gap. On this model, we introduce the lattice effects, which induce the periodic potential and break the translational invariance of the boundary field theory. Without the lattice, due to the translational invariance and the mass term, there is a delta function peak at zero frequency on the AC conductivity. We study how this delta function peak is inuenced by the lattice effects, which we introduce perturbatively. In the probe limit, we evaluate the perturbative corrections to the conductivities at very small frequency limit. We find that the delta function peak remains, even after the lattice effects are introduced, although its weight reduces perturbatively. We also study the lattice wavenumber dependence of this weight. Our result suggests that in the U(1) symmetry breaking phase, the delta function peak is stable against the lattice effects at least perturbatively.

KW - AdS-CFT Correspondence

KW - Gauge-gravity correspondence

KW - Holography and condensed matter physics (AdS/CMT)

UR - http://www.scopus.com/inward/record.url?scp=84870364578&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870364578&partnerID=8YFLogxK

U2 - 10.1007/JHEP11(2012)117

DO - 10.1007/JHEP11(2012)117

M3 - Article

VL - 2012

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 11

M1 - 117

ER -